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Abstract

A conceptual lab-in-a-photonic-crystal biosensor is demonstrated that can multiplex four or more distinct disease-markers and distinguish their presence and combinations simultaneously with unique spectral fingerprints. This biosensor consists of a photonic-band-gap, multi-mode waveguide coupled to surface modes on either side, encased in a glass slide with microfluidic channels. The spectral fingerprints consist of multiple peaks in optical transmission vs. frequency that respond sensitively and uniquely in both frequency shift and nonmonotonic change of peak transmittance levels to various analyte bindings. This special property enables complete, logical determination of twelve different combinations of four distinct disease-markers through one scan of the transmission spectrum. The results reveal unique phenomena such as switching between the strong-coupling and weak-coupling combinations of surface states by analyte binding at different locations along the central waveguide. The unconventional transmission spectra are explained using a Landauer-Büttiker, multiple-scattering, transmission theory that reproduces the main features of the exact finite-difference-time-domain simulation.

Figures (18)

Illustration of photonic crystal biosensor. The blue regions at the left and right sides are glasses. The surface layers are elliptical shaped to support surface modes. The distance between the center of the surface micro-pillars and the glass is a. The waveguide mode is introduced by a larger micro-pillar with radius 0.445a where a is the center-to-center distance between adjacent micro-pillars. The radius of normal micro-pillars is 0.25a. Adjacent elliptic micro-pillars at the surface have the same semi-minor axis 0.15a, while their semi-major axes are 0.25a and 0.28a, respectively. Three different types of disease markers α, β, and σ are attached to three different analyte binding sites (labeled as “L”, “R”, and “W” in the figure) at the left surface, the right surface, and the central waveguide layer, separately. The length of the photonic crystal in the y direction can be l = 3 (as shown in the figure) or l = 4 (not shown).

(a) Band structure of the photonic crystal sensor. The blue shaded regions denote the bulk photonic bands. The red (dashed), green (dotted) and blue (solid) curves in the PBG stand for the waveguide and (two) surface guided modes, separately. The yellow solid line denotes the light line in glass. Period doubling in the x direction folds the region
π2a<qx≤πa back to the first Brillouin zone
−π2a<qx≤π2a. As a consequence the surface and waveguide modes originally below the light line are moved to above the light line which are then able to couple to light in glass. Since the structure possess left-right mirror symmetry, the two surface modes form the anti-symmetric (blue curve) and symmetric (green curve) modes, respectively. The field distribution of the waveguide and surface modes are illustrated in (c)–(e). The frequencies of the anti-symmetric surface mode, the symmetric surface mode and the waveguide mode at qx = 0 are 0.2605, 0.2613 and 0.2640 (in unit of
2πca) separately. The length of the photonic crystal in the y direction is l = 3.

Transmission responses to analyte binding for different binding configurations. The right-most peak is dominated by the central waveguide mode, whereas the central peak arises from the weak-coupling surface mode, and the left-most peak is dominated by the strong-coupling surface mode. (a) When analyte σ is bound to the W site at the central waveguide. (b) When analyte α is bound to the L site at the left surface of the photonic crystal. (c) When analytes α and β bind to the L and R sites at the surfaces with equal thickness. (d) When analytes α and σ bind to both the L and W sites. From red, blue, green to black, the thickness of analyte layer is 0, 0.05a, 0.1a, and 0.15a, respectively. For (a) and (c), the system has mirror symmetry and the strong-coupling (weak-coupling) surface mode is the anti-symmetric (symmetric) combination of the left and right surface modes. In comparison, for (b) and (d), the mirror symmetry is broken, the strong-coupling (weak-coupling) surface mode is no longer the anti-symmetric (symmetric combination of the left and right surface modes, but other mixture of the two. The length of the photonic crystal along the y direction is l = 3.

(a) Illustration of photonic crystal sensor with two central waveguide modes and enlarged unit cell. Four different analyte binding sites are labeled as “L”, “W1”, “W2”, and “R”. The radii of the two enlarged micro-pillars in the middle are r1 = 0.47a (W1) and r2 = 0.455a (W2), respectively. (b) and (c): Electric field Ez distribution of the waveguide and surface modes from plane-wave-expansion calculation for the case with no analyte binding. At qx = 0, the w1 waveguide mode has frequency 0.2591(
2πca), the w2 waveguide mode has frequency 0.2628(
2πca), the anti-symmetric surface mode has frequency 0.2614(
2πca), and the symmetric surface mode has frequency 0.2618(
2πca). Note that these frequencies are slightly different from the peak frequencies in the FDTD calculation. The length of the photonic crystal in the y direction is l = 4. The structure is periodically repeated in the x (vertical) direction.

Electric field Ez distributions of the (a) central waveguide modes and (b) surface modes (from plane-wave-expansion calculations) for the case with disease marker σ2 binding to the W2 site with thickness 0.2a. At qx = 0, the upper waveguide mode (w1) has frequency 0.2591(
2πca), while the lower waveguide mode (w2) has frequency 0.2619(
2πca). The anti-symmetric surface mode has frequency 0.2613(
2πca), while the symmetric surface mode has frequency 0.2618(
2πca). Note that these frequencies are slightly different from the peak frequencies obtained by FDTD simulations.

Transmission spectra for different three-analyte binding combinations: (a) analytes are bound to all sites with equal thickness, (b) analytes are bound to all except the W2 site with equal thickness, (c) analytes are bound to all except the W1 site with equal thickness. From the red, blue, green, orange, and black curves in each figure represent different thicknesses of disease markers: (a) 0.05a, 0.1a, 0.12675a, 0.15a, and 0.2a; (b) 0.025a, 0.05a, 0.0827a, 0.1a, and 0.15a; (c) 0.025a, 0.05a, 0.0828a, 0.1a, and 0.15a.

Electric field Ez distributions of the (a) central waveguide modes and (b) surface modes from plane-wave-expansion calculations for the case with analytes binding to the L, W1, and W2 sites with equal thickness 0.15a. At qx = 0, the upper waveguide mode (w1) has frequency 0.2590(
2πca), the lower waveguide mode (w2) has frequency 0.2620(
2πca), the left surface mode has frequency 0.2603(
2πca), and the right surface mode has frequency 0.2616(
2πca). These frequencies are slightly different from the peak frequencies obtained by FDTD simulations.

Importance of surface-waveguide coupling is demonstrated via the peak transmittance at the two surface modes when the disease marker α is attached to the left surface (the L binding site) for (a) l = 3 and (b) l = 4 chip. The solid curves (red and blue) are for structures with the (single-mode) central waveguide, whereas the dashed curves (black and green) are for structures without the central waveguide. Curves with • stands for peak transmittance at the lower frequency surface mode, whereas curves with △ represent peak transmittance at the higher frequency surface mode. The vertical axis of (b) is on log-scale.

Tables (2)

Table 1 Diagnostic logic table using three disease markers in the l = 3 biosensor with a single central waveguide mode. Changes in peak frequencies and transmittance in response to various analyte-binding configurations are tabulated. The frequency shift of the waveguide mode, Ωw, (right peak), the strong-coupling surface mode, Ωsc, (left peak), and the weak-coupling surface mode, Ωwc, (central peak), together with changes in peak transmission levels, Tsc and Twc, of the latter two surface modes, provide distinct spectral fingerprints of different analyte-binding configurations. The symbol ↓:↑ denotes that peak transmission first decreases then increases.

Table 2 Logic table for enhanced medical diagnosis using four disease markers in the l = 4 biosensor with two central waveguide modes. Here we show how the peak frequencies and transmission levels change in response to the increase of analyte-layer thickness for the 12 analyte-binding configurations. The leftmost, middle-left, middle-right, and rightmost peaks in the transmission spectrum are denoted as w1, s1, s2, and w2. Their frequencies are denoted as Ωw1, Ωs1, Ωs2, and Ωw2, and their peak transmission levels are denoted as Tw1, Ts1, Ts2, and Tw2. We use the symbol ↓:↑ to represent that the transmission level first decreases then increases.

Metrics

Table 1

Diagnostic logic table using three disease markers in the l = 3 biosensor with a single central waveguide mode. Changes in peak frequencies and transmittance in response to various analyte-binding configurations are tabulated. The frequency shift of the waveguide mode, Ωw, (right peak), the strong-coupling surface mode, Ωsc, (left peak), and the weak-coupling surface mode, Ωwc, (central peak), together with changes in peak transmission levels, Tsc and Twc, of the latter two surface modes, provide distinct spectral fingerprints of different analyte-binding configurations. The symbol ↓:↑ denotes that peak transmission first decreases then increases.

Analyte-binding configuration

Ωw

Ωsc

Ωwc

Tsc

Twc

no binding

|

|

|

—

—

σ binding only

←

|

|

—

—

(α ⊕ β) & (¬ σ)

|

←

←

↓

↓:↑

(α ⊕ β) & σ

←

←

←

↓

↓:↑

(α & β) & (¬ σ)

|

←

←

—

—

α & β & σ

←

←

←

—

—

Table 2

Logic table for enhanced medical diagnosis using four disease markers in the l = 4 biosensor with two central waveguide modes. Here we show how the peak frequencies and transmission levels change in response to the increase of analyte-layer thickness for the 12 analyte-binding configurations. The leftmost, middle-left, middle-right, and rightmost peaks in the transmission spectrum are denoted as w1, s1, s2, and w2. Their frequencies are denoted as Ωw1, Ωs1, Ωs2, and Ωw2, and their peak transmission levels are denoted as Tw1, Ts1, Ts2, and Tw2. We use the symbol ↓:↑ to represent that the transmission level first decreases then increases.

Analyte-binding configuration

Ωw1

Ωs1

Ωs2

Ωw2

Tw1

Ts1

Ts2

Tw2

No binding

|

|

|

|

—

—

—

—

σ1 binding only

←

|

|

|

—

—

—

—

σ2 binding only

|

←

|

←

—

↓

—

↓

(α & β) & (¬σ1) & (¬σ2)

|

←

←

|

↓

↓

↑

↑

(α ⊕ β) & (¬σ1) & (¬σ2)

|

←

|

|

↓

↓:↑

↓:↑

↑

(α ⊕ β) & σ1 & (¬σ2)

←

←

|

|

↓

↓:↑

↓:↑

↑

(α ⊕ β) & (¬σ1) & σ2

|

←

|

←

↓

↓:↑

↓:↑

|

(¬α) & (¬β) & σ1 & σ2

←

←

|

←

—

↓

—

↓

(α ⊕ β) & σ1 & σ2

←

←

|

←

↓

↓:↑

↓:↑

—

α & β & σ1 & σ2

←

←

←

←

↓

↓

↑

↑

α & β & σ1 & (¬σ2)

←

←

←

|

↓

↓

↑

↑

α & β & (¬σ1) & σ2

|

←

←

←

↓

↓

↑

↑

Tables (2)

Table 1

Diagnostic logic table using three disease markers in the l = 3 biosensor with a single central waveguide mode. Changes in peak frequencies and transmittance in response to various analyte-binding configurations are tabulated. The frequency shift of the waveguide mode, Ωw, (right peak), the strong-coupling surface mode, Ωsc, (left peak), and the weak-coupling surface mode, Ωwc, (central peak), together with changes in peak transmission levels, Tsc and Twc, of the latter two surface modes, provide distinct spectral fingerprints of different analyte-binding configurations. The symbol ↓:↑ denotes that peak transmission first decreases then increases.

Analyte-binding configuration

Ωw

Ωsc

Ωwc

Tsc

Twc

no binding

|

|

|

—

—

σ binding only

←

|

|

—

—

(α ⊕ β) & (¬ σ)

|

←

←

↓

↓:↑

(α ⊕ β) & σ

←

←

←

↓

↓:↑

(α & β) & (¬ σ)

|

←

←

—

—

α & β & σ

←

←

←

—

—

Table 2

Logic table for enhanced medical diagnosis using four disease markers in the l = 4 biosensor with two central waveguide modes. Here we show how the peak frequencies and transmission levels change in response to the increase of analyte-layer thickness for the 12 analyte-binding configurations. The leftmost, middle-left, middle-right, and rightmost peaks in the transmission spectrum are denoted as w1, s1, s2, and w2. Their frequencies are denoted as Ωw1, Ωs1, Ωs2, and Ωw2, and their peak transmission levels are denoted as Tw1, Ts1, Ts2, and Tw2. We use the symbol ↓:↑ to represent that the transmission level first decreases then increases.